Optimizing the observingbandwidths for the CLASS

HF detectorsK. Randle1,2 K. Rostem3 D. Chuss2

1Department of PhysicsUniversity of Massachusetts Amherst

2Observational Cosmology LaboratoryNASA Goddard Spaceflight Center

3Department of Physics and AstronomyJohns Hopkins University

25 July 2014SPS Summer Intern Symposium

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Events in the Early Universe

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Imprints of Inflation on the CosmicMicrowave Background

• Small fluctuations in the early moments of the universebecome anisotropies in temperature of the CMB, 2.7260 ±0.0013 K

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Imprints of Inflation on the CosmicMicrowave Background

• Process of inflation yieldslarge gravitational waves

• GW’s uniquely causeB-mode polarization

• Therefore, a B-mode signalin the CMB would beevidence for inflation

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Imprints of Inflation on the CosmicMicrowave Background

• Process of inflation yieldslarge gravitational waves

• GW’s uniquely causeB-mode polarization

• Therefore, a B-mode signalin the CMB would beevidence for inflation

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Imprints of Inflation on the CosmicMicrowave Background

• Process of inflation yieldslarge gravitational waves

• GW’s uniquely causeB-mode polarization

• Therefore, a B-mode signalin the CMB would beevidence for inflation

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Detecting the CMB

• The Cosmology Large Anuglar Scale Surveyor (CLASS)will use very sensitive, very cold bolometers at fourdifferent frequencies in order to detect the verylow-frequency microwave photons from the CMB.

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Avoiding Other Sources

• Optical filters, feed horns, waveguides and on-chip filtersremove frequencies beyond the desired signal.

• Location in the Atacama desert will decrease microwavesignal from the atmosphere

• The Variable Polarization Modulator distinguishes thepolarization of the photons

Randle, Rostem, Chuss CLASS Bandwidth Optimization

The Atmospheric Signal

Data from Refs. [1] and [2]

• The atmosphere behaves like a black body - absorbing andemitting - at about 270 K

Randle, Rostem, Chuss CLASS Bandwidth Optimization

The Atmospheric Signal

Data from Refs. [1] and [2]

• It doesn’t absorb and emit on all frequencies, but where itabsorbs, it emits; where it doesn’t absorb, it doesn’t emit

Randle, Rostem, Chuss CLASS Bandwidth Optimization

The Atmospheric Signal

Data from Refs. [1] and [2]

• The waveguides only permit transmission of photons atcertain wavelengths

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Bandwidth Optimization Goals

To determine the optimal bandwidth for on-chip filter placement:

• Maximize power from the CMB• Minimize noise from the signal• Use a model based on variable atmospheric transmission

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Mathematical Basis - Power

Planck’s law (intensity per frequency)

Bν(T ) =2hν2

c21

ehνkBT − 1

(1)

Power per frequency, Approximating AΩ = λ2 (Ref. [3])

p(ν) = AΩBν(T ) = αεf2hν

ehνkBT − 1

(2)

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Mathematical Basis - Noise

Variance per frequency

σ2 = 〈n2〉 − 〈n〉2 (3)

Derived for radio-frequency bolometers in Ref. [4]:

NEP 2 =4h2ν2(αεf)

ehνkBT − 1

(1 +

αεf

ehνkBT − 1

)(4)

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Weighting by PWV

Since the water in the atmosphere is variable and influencesatmospheric transmissivity, I weighted the power and noise bythe PWV on a Rayleigh distribution.

D =x

σ2e

−x22σ2 (5)

Given the percent of time the Atacama is below a set of PWVs,I performed a χ2 test to evaluate σ = 1.056251.

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Optimization map

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Results

The maxima represent the bandwidths with the highest CMBsignal and the lowest noise and yield the following results.

Band Recommended Band Total Power Total NEP90GHz 75.2 to 108.8GHz 4.9781 pW 3.4497 · 10−5 pW/

√Hz

150GHz 125.5 to 164.7GHz 7.0871 pW 5.0195 · 10−5 pW/√Hz

220GHz 187.1 to 239.0GHz 13.6861 pW 8.9116 · 10−5 pW/√Hz

Randle, Rostem, Chuss CLASS Bandwidth Optimization

Acknowledgements

Special thanks to the SPS Internship Program who funded mefor this research. Thank you to my advisors and colleagues atNASA Goddard Spaceflight Center, Dr. David Chuss, Dr.Karwan Rostem, Felipe Colazo, and Kyle Helson. Thanks to theSPS staff for their support and guidance.

Randle, Rostem, Chuss CLASS Bandwidth Optimization

References

1. ALMA Collaboration, Atmosphere model based on JuanPardo’s ATM model for the altitude of the Atacama Desert,almascience.eso.org/about-alma/weather/atmosphere-model

2. K. U-Yen, High Frequency Structure Simulations for theCLASS waveguides.

3. J. Kraus, R. Marhefka, Antennas (McGraw-Hill, 2001)International Edition, Chap. 2.

4. J. Mather, "Bolometer noise: nonequelibrium theory," Appl.Opt. 21, 1125-1129 (1982).

5. W. Press, B. Flannery, W. Vetterling, S. Teukolsky,Numerical Recipes in Pascal: The Art of ScientificComputing. (Cambridge University Press, 1989). p. 122

Randle, Rostem, Chuss CLASS Bandwidth Optimization